Renormalization Methods: A Guide For Beginners

Paperback | December 7, 2007

This book is unique in occupying a gap between standard undergraduate texts and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretation (and motivation), including mean-field theories and high-temperature and low-densityexpansions. It then proceeds by easy steps to the famous epsilon-expansion, ending up with the first-order corrections to critical exponents beyond mean-field theory. Nowadays there is widespread interest in applications of renormalization methods to various topics ranging over soft condensedmatter, engineering dynamics, traffic queueing and fluctuations in the stock market. Hence macroscopic systems are also included, with particular emphasis on the archetypal problem of fluid turbulence. The book is also unique in making this material accessible to readers other than theoreticalphysicists, as it requires only the basic physics and mathematics which should be known to most scientists, engineers and mathematicians.

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This book is unique in occupying a gap between standard undergraduate texts and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretation (and motivation), including mean-field theories and high-temperature and low-densityexpansions. It then proceeds by easy steps to ...

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Table of Contents

What is renormalization?1. The bedrock problem: why we need renormalization methods2. Easy applications of renormalization group (RG) to simple models3. Mean-field theories for simple modelsRenormalized perturbation theories (RPT)4. Perturbation theory using a control parameter5. Classical nonlinear systems driven by random noise6. Application of RPT to turbulence and related problemsRenormalization group7. Setting the scene: critical phenomena8. Real-space RG9. Momentum-space RG10. Field-theoretic RG11. Dynamical RG applied to classical nonlinear systemsAppendicesA. Statistical ensemblesB. From statistical mechanics to thermodynamicsC. Exact solutions in one and two dimensionsD. Quantum treatment of the Hamiltonian N-body assemblyE. Generalization of the Bogoliubov variational method to a spatially-varying magnetic field

Editorial Reviews

`I think this book is the best introductory textbook on techniques of renormalization available. It will be a delight to read for anyone who is encountering the topic for the first time and is wishing to exploit the methods to pass an exam or in one's field.'Contemporary Physics